量子博弈論中理論與實踐的橋接：在NISQ硬體上實現性別之戰的優化與誤差緩解

摘要

在實際硬體上實現量子博弈論面臨著噪音、退相干以及量子比特連接性有限等挑戰，然而此類實驗驗證對於理論預測的確認至關重要。我們在IBM Quantum的ibm sherbrooke超導處理器上，首次完整實驗實現了基於Eisert-Wilkens-Lewenstein（EWL）框架的“性別之戰”博弈。通過在[0, π]範圍內31個糾纏值γ下，對四種量子策略（I、H、R(π/4)、R(π)）進行了每種配置2048次測量的評估，從而實現了理論預測與硬體執行之間的直接比較。為減輕噪音和變異性，我們引入了一種引導式電路映射（GCM）方法，該方法基於實時拓撲和校準數據動態選擇量子比特對並優化路由。理論模型預測相較於經典均衡可帶來高達108%的收益提升，儘管硬體引入了一定偏差，但採用GCM的實驗結果仍將預期收益趨勢的相對誤差控制在3.5%-12%以內。這些發現表明，在現實的NISQ（含噪中尺度量子）條件下，戰略協調中的量子優勢依然能夠保持，為量子博弈論在多智能體、經濟及分佈式決策系統中的實際應用開闢了道路。

English

Implementing quantum game theory on real hardware is challenging due to noise, decoherence, and limited qubit connectivity, yet such demonstrations are essential to validate theoretical predictions. We present one of the first full experimental realizations of the Battle of the Sexes game under the Eisert-Wilkens-Lewenstein (EWL) framework on IBM Quantum's ibm sherbrooke superconducting processor. Four quantum strategies (I, H, R(pi/4), R(pi)) were evaluated across 31 entanglement values gamma in [0, pi] using 2048 shots per configuration, enabling a direct comparison between analytical predictions and hardware execution. To mitigate noise and variability, we introduce a Guided Circuit Mapping (GCM) method that dynamically selects qubit pairs and optimizes routing based on real-time topology and calibration data. The analytical model forecasts up to 108% payoff improvement over the classical equilibrium, and despite hardware-induced deviations, experimental results with GCM preserve the expected payoff trends within 3.5%-12% relative error. These findings show that quantum advantages in strategic coordination can persist under realistic NISQ conditions, providing a pathway toward practical applications of quantum game theory in multi-agent, economic, and distributed decision-making systems.

量子博弈論中理論與實踐的橋接：在NISQ硬體上實現性別之戰的優化與誤差緩解

Bridging Theory and Practice in Quantum Game Theory: Optimized Implementation of the Battle of the Sexes with Error Mitigation on NISQ Hardware

摘要

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